If you are found to be eligible to take part in this study, you will be assigned to a either Arm A or Arm B based when you joined this study, the disease type, and the drugs you have taken in the past. Up to 5 dose levels of the study drug will be tested in each arm. Up to 6 participants will be enrolled in each dose level of arms A and B. The first group of participants in Arm A will receive the FDA approved dose of crizotinib plus the lowest dose level of dasatinib. The first group of participants in Arm B will receive the FDA approved dose of dasatinib plus the lowest dose level of crizotinib. Each new group will receive a higher dose of the study drug combination than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of the study drug combination is found.